High Mass Flow Rate in a BAL Outflow of Quasar SDSS J1130+0411

In order to measure the width of the C iv BAL, measure the width of the C iv emission line (see Section 5.1), and determine the redshift of J1130+0411, we retrieved an SDSS spectrum from MJD=52642 (January 3, 2003). Figure 2 shows this unnormalized spectrum with the main absorption troughs labeled. Note that the vertical lines are not centered in many of the BALs. The high column density of these ions allows for higher velocities in the outflow, thus widening the blue side of the BAL. Additionally, S4 is blended with the blue side of these BALs.

For J1130+0411 we determine a systemic redshift $z=3.98$ that lines up with the C ii/C ii* and Si iv emission lines. As an additional check, this redshift places the Ly $\alpha$ line $\sim 6$ Å blueward of the edge of the Lyman $\alpha$ forest in the rest frame. This estimate is different from the one made by Chen et al. (2021), who determine a redshift of $z=3.930$ that appears to instead line up with the BAL outflow. Chen et al. (2021) also identify one C iv absorption system. Using their reported redshift to calculate absorption system velocities, we find that this system best matches our highest velocity system, S1. They did not identify S5, as this C iv absorption falls in the spectral gap of this UVES data ($7521-7666$ Å observed wavelength).

Our redshift is also different from the redshift reported on the SDSS website, $z=5.25$. SDSS uses an algorithm in order to determine the redshift of objects in its catalog, and this algorithm does not always produce accurate measurements. It is clear by eye that their reported redshift does not coincide with any emission features in the unnormalized spectrum.

The first step in determining the physical characteristics of an outflow is to determine the column densities of the ions observed in the system. The simplest way of doing this is to use the apparent optical depth (AOD) method, which assumes that the outflow completely and uniformly covers the source (Savage & Sembach, 1991). In this case, the normalized flux is related to the optical depth by

where $I$ is the observed flux and $\tau$ is the optical depth. The column density can found by

where $m_{e}$ is the electron mass, $c$ is the speed of light, $e$ is the elementary charge, and $f$ and $\lambda$ are the oscillator strength and wavelength of the transition line, respectively. This method only gives a lower limit to the column density. If an ion presents as a doublet or multiplet, we can use the more accurate partial covering (PC) method (Barlow et al. 1997; Arav et al. 1999a, b), which accounts for effects such as non-black saturation (Edmonds et al. 2011; Borguet et al. 2012). This method introduces a velocity-dependent covering fraction $C(v)$ (de Kool et al. 2002; Arav et al. 2005), and the normalized flux depends on the optical depth by

where $I_{1}$ and $I_{2}$ are the normalized fluxes of the doublet transition lines, and $R_{21}=f_{2}\lambda_{2}/f_{1}\lambda_{1}$. Here, $f_{1}$, $f_{2}$, $\lambda_{1}$, and $\lambda_{2}$ are the oscillator strengths and wavelengths of the two doublet lines. We adopt column densities calculated using PC rather than AOD whenever possible.

Many of the absorption lines are blended with other troughs, so we model each trough by fitting to an unblended section of the trough a Gaussian of the form

where, for trough $i$, $A_{i}$ is the scaling factor, $\sigma_{i}$ is the velocity dispersion ($\mathrm{FWHM}=2\sigma\sqrt{2\mathrm{ln}(2)}$), and $v_{i}$ is the velocity centroid. For example, in many cases the blue wing of the trough is the only unblended portion and therefore is what the Gaussian is fitted to. For S5 in particular, we observe both a wide and a narrow component in most lines, so for this system we use a double Gaussian to fit the troughs, i.e., $I_{i}=I_{\mathrm{wide}}\times I_{\mathrm{narrow}}$.

Compared with Si ii $1260$ Å and $1304$ Å, the Si ii $1808$ Å trough is shallow and narrow, and so we assume it is unsaturated and interpret its AOD column density as a measurement rather than a lower limit. We observe non-black saturation in the Al iii $\lambda\lambda 1854,1860$ BAL, so we obtain a measurement for its column density using the PC method. For all other BALs, we use the AOD method to obtain a lower limit. Table 2 gives the column densities we adopted in this analysis. We add 20% error in quadrature to the column density errors in order to account for uncertainty in the continuum model (Xu et al., 2018). Note that the adopted Fe ii column density is somewhat higher than that of the AOD value. This is because four of the Fe ii* energy levels show more than one trough for the same level, and so for these we use the PC solution. We then add these measurements to the AOD measurements of the remaining levels in order to calculate the total Fe ii column density.

In order to determine $N_{H}$ and $U_{H}$, we use the spectral synthesis code Cloudy (version c17.00, Ferland et al. 2017) to create photoionization models with a given hydrogen column density ($N_{H}$) and ionization parameter ($U_{H}$), following previous works (e.g., Xu et al. 2019; Miller et al. 2020a, b; Byun et al. 2022a, b). For these models we assume solar metallicity and the spectral energy distribution (SED) of quasar HE0238-1904 (Arav et al. 2013, see their Figure 10). Together, these parameters determine the column density of each ion in a photoionization model. We can therefore create a grid of models over a range of $N_{H}$ and $U_{H}$ and compare them to our measured ionic column density. The model with the lowest $\chi^{2}$ gives a solution that best matches our observations. The best-fit solution for S5 gives us $\log N_{H}=21.34_{-0.33}^{+0.24}$ cm^-2 and $\log U_{H}=-1.75_{-0.45}^{+0.28}$. The "Adopted" column of Table 2 lists the column densities used for this fit. Figure 3 shows a visualization of this solution.

The ratios of excited state to ground state column densities can be used to determine the electron number density of an absorber (Moe et al., 2009). This can become difficult to measure directly if the ground or excited state troughs in a spectrum are significantly blended, or if the ground state trough is saturated. In this case, we can use the Synthetic Spectral Simulation method (SSS) in order to help determine $n_{e}$ (Xu et al., 2020a). For this method, we input the previously obtained photoionization solution, with a range of $n_{e}$, into Cloudy to get the total column densities of the desired ions. From the wavelength, oscillator strength, excited ionic critical densities, and output column density of each absorption line, we create synthetic, theoretical spectra with the range of $n_{e}$. We then find the synthetic spectrum that best matches the observed spectrum in order to determine the best fit $n_{e}$ for that absorption system. Since we use a fixed metallicity and SED, $N_{H}$ affects the total strength of all lines, and $U_{H}$ affects the relative strength between different ions. Excited ions are mostly populated by collisions between free electrons and ground state ions (Osterbrock & Ferland, 2006), so $n_{e}$ affects the relative strength between the ground state and various excited states of ions.

Table 3 gives a determination of $n_{e}$ for S5 of J1130+0411 and Figure 4 shows the SSS plots used to find this solution. Note that these fits have a high reduced $\chi^{2}$ (also given in Figure 4). Certain phenomena unrelated to fitting $n_{e}$ contribute to this, such as the unidentified line at observed wavelength $7968$ Å in the left plot of Figure 4 and the atmospheric lines from $8932-8970$ Å in the right plot. However, the largest contribution to this $\chi^{2}$ comes from the fact that the best fit SSS method overpredicts the strength of the Fe ii* $1873\ \mathrm{cm}^{-1}$ energy level transitions and underpredicts the strength of all other Fe ii* energy level transitions, resulting in a poor fit overall. This discrepancy is discussed further in Section 5.2. In order to determine the positive and negative errors, we increase and decrease (respectively) the input $n_{e}$ until the simulated spectrum has double the $\chi^{2}$ compared with the best fit. From the SSS method we determine $\log n_{e}=2.6_{-0.7}^{+0.8}$ cm^-3. We also note that increasing $N_{H}$ by $0.1$ dex slightly increases the quality of the fit, so we adopt for this system $\log N_{H}=21.44_{-0.33}^{+0.24}$ cm^-2.

The thin, elliptical shape of the photoionization solution (see Figure 3) demonstrates that the $N_{H}$ and $U_{H}$ errors are correlated with each other. In order to see how this could affect our error estimates, we calculate three values $\zeta^{+}$, $\zeta$, and $\zeta^{-}$ that correspond to the top-right corner, middle solution, and bottom-left corner of the photoionization solution contour, respectively, so that $\dot{M}=\zeta*\sqrt{Q_{H}/n_{e}}$:

where $\sigma_{N_{H}}^{+}$, $\sigma_{N_{H}}^{-}$, $\sigma_{U_{H}}^{+}$, and $\sigma_{U_{H}}^{-}$ are the positive and negative errors for $N_{H}$ and $U_{H}$ given in Table 3. Now, we want to make sure that $\zeta^{+}>\zeta$ and $\zeta^{-}<\zeta$. Since $\zeta\propto N_{H}/\sqrt{U_{H}}$, this requires satisfying the following condition:

If these inequalities do not hold, then we simply swap the definitions of $\zeta^{+}$ and $\zeta^{-}$. Finally, we define $\sigma_{\zeta}^{+}=\zeta^{+}-\zeta$ and $\sigma_{\zeta}^{-}=\zeta-\zeta^{-}$ and add to this in quadrature the errors of $n_{e}$ and $Q_{H}$:

where the factor of $1/4$ comes from the fact that $R$ is proportional to the square root of $n_{e}$ and $Q_{H}$. In the end, for S5, this method produces errors that are a factor of $\sim 1.3$ lower than those calculated by simply adding the $R$ and $N_{H}$ errors in quadrature.

In order to numerically compare our calculated $\dot{E}_{k}$ with $L_{\mathrm{Edd}}$, we must first determine $L_{\mathrm{Edd}}$ for J1130+0411. To do this, we take advantage of a method introduced by Coatman et al. (2016), in which they use the width of the C iv emission line to determine the mass of the black hole (see their Equations 4 & 6). This method is based on that used by Vestergaard & Peterson (2006). Modelling the C IV emission in this object is difficult as it is heavily blended with absorption. However, it is the only emission feature visible in the spectrum of J1130+0411 that we can use to determine the black hole mass. So, to approach this we center a Gaussian on the C iv $\lambda 1549$ Å emission line and fit it to an unblended portion of the red wing in order to get the full width at half maximum (FWHM). Figure 5 shows this Gaussian fit. From there it is simple to calculate $L_{\mathrm{Edd}}$ (Osterbrock & Ferland, 2006), and we derive for this system $L_{\mathrm{Edd}}=9.7_{-1.4}^{+1.7}\times 10^{47}$ erg s^-1. Our calculated $\dot{E}_{k}$ for S5 is then $1.4_{-0.8}^{+2.2}$% of the $L_{\mathrm{Edd}}$ of J1130+0411. This is above the $0.5$% threshold suggested by Hopkins & Elvis (2009), thus we conclude that the main system has the potential to contribute to AGN feedback.

Other observations of outflows containing Fe ii* absorption have been performed. In SDSS J1439-0106, Byun et al. (2022a) compare the abundance ratios of five different Fe ii* energy levels to the ground state and find that the $1873\ \mathrm{cm}^{-1}$ level is in agreement with the other four. Xu et al. (2021) measure multiple excited Fe ii energy levels up to $21,580\ \mathrm{cm}^{-1}$ in Q0059-2735, however no $1873\ \mathrm{cm}^{-1}$ troughs were reported. Choi et al. (2020) also report multiple excited states with the exclusion of $1873\ \mathrm{cm}^{-1}$ in SDSS J1352+4239. Several excited levels are measured in QSO 2359-1241 by Korista et al. (2008), including three $1873\ \mathrm{cm}^{-1}$ lines: $2332$ Å, $2349$ Å, and $2361$ Å. However as they note, these troughs are blended with other lines. All of these lines are out of range of the J1130+0411 data. It appears that the Fe ii $2332$ Å, $2349$ Å, $2361$ Å, and $2494$ Å lines detected in FBQS 0840+3633 by de Kool et al. (2002) are of the $1873\ \mathrm{cm}^{-1}$ excited level, but these are also heavily blended and out of the spectral range of J1130+0411.

Blending of Fe ii* $1873\ \mathrm{cm}^{-1}$ with other Fe ii lines is also a problem in J1130+0411. Although this is somewhat mitigated by using the SSS method, this method is not perfect, and assumes an AOD scenario for every trough. The spectral synthesis procedure SimBAL (Leighly et al., 2018) provides a similar approach to SSS, but instead implements a power law method (Arav et al., 2005; Leighly et al., 2019) in order to create synthetic spectra. Future studies could use SimBAL to attempt to model the Fe ii lines in J1130+0411 in that way.

We also note that the average mass flow rate of $\dot{M}=4100_{-2400}^{+6600}$ $M_{\odot}$ yr^-1 is particularly large. Byun et al. (2022b) find an even higher mass flow rate of $6500_{-3400}^{+8900}$ $M_{\odot}$ yr^-1 in their S2 of quasar SDSS J0242+0049. These rates are roughly ten times greater than the highest of which reported by Choi et al. (2022), with the largest in their sample, J1154+0300, having only $\dot{M}\sim 500$ $M_{\odot}$ yr^-1. Comparing J1130+0411 with relatively similar objects in this sample, we conclude that our larger $\dot{M}$ can be attributed to both a higher outflow velocity and outflow distance in S5. Our $L_{\mathrm{bol}}=9.2_{-0.5}^{+0.5}\times 10^{47}$ erg s^-1 is higher than the largest bolemetric luminosity in the Choi et al. (2022) sample by $\sim 0.5$ dex, and our $\log\dot{E}_{k}=46.13_{-0.37}^{+0.41}$ is comparable to the the highest values in their sample. Additionally of note, the systemic redshift $z=3.98$ of J1130+0411 is significantly higher than the lower redshift quasars, with $0.66<z<1.63$, targeted by Choi et al. (2022).

We identify seven absorption systems in this quasar other than the main system. We order these in terms of decreasing velocity, so that S1 ($-15,400$ km s^-1) is the highest velocity system and S8 ($-2400$ km s^-1) is the lowest velocity system. S1 was identified by Chen et al. (2021) (see Section 2.1). The presence of wide, smooth C iv troughs and the unblended red Si iv trough lead us to believe that this system is an outflow. S2 has C iv and Si iv troughs, but as they are very narrow, this is most likely an intervening system. Although we observe C ii* in S3, the fact that we do not observe any Si iv is again indicative of an intervening system. Many of the expected lines in S4 fall in the blue end of the S5 BALs, leading us to believe that this system is actually subcomponent of S5. S5 is the main system discussed in the bulk of this paper. In S6, we see some excited state ions, though blended, and many of the ions we expect to see in quasar outflows, so this system is most likely an outflow. S7 and S8 also show (blended) C ii* troughs, so these are most likely outflows as well.

Unfortunately, all of these systems aside from S5 have few unblended diagnostic troughs from which to extract reliable ionic column densities. In addition, no unblended excited troughs are identified in any of these weaker systems. Therefore, while we are able to get some information about $N_{H}$ and $U_{H}$ for some systems, we are not able to extract any electron number densities, and so we are not able to calculate any distances or energetics for these systems. Table 1 summarizes the properties of these systems that we were able to measure. Since S2 and S3 are intervening and thus their redshifts are likely cosmological, these redshifts are reported rather than their velocities in the footnotes of this table.